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Popular >

integral from 2 to 6 of (6x+2)^2

Solution

\int_{2}^{6} (6 x + 2)^{2} d x

Solution

2896

Solution steps

\int_{2}^{6} (6 x + 2)^{2} d x

Expand

(6 x + 2)^{2} : 36 x^{2} + 24 x + 4

= \int_{2}^{6} 36 x^{2} + 24 x + 4 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{2}^{6} 36 x^{2} d x + \int_{2}^{6} 24 x d x + \int_{2}^{6} 4 d x

\int_{2}^{6} 36 x^{2} d x = 2496

\int_{2}^{6} 24 x d x = 384

\int_{2}^{6} 4 d x = 16

= 2496 + 384 + 16

Simplify

= 2896

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 2 to 6 of (6x+2)^2 ?
The integral from 2 to 6 of (6x+2)^2 is 2896